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Title: Equations on the Wasserstein space and applications

Abstract:听The study of differential equations on the Wasserstein space of probability measures has become an active area of research in recent years. One motivating factor is that many relevant observable quantities in interacting agent systems have mean field approximations that solve such equations, as has been borne seen in mean field games/control theory as well as applications in statistical physics. A well-posedness theory for these equations can thus lead to new methods for studying such mean field models. In this talk, we present some well-posedness results for Hamilton-Jacobi equations on Wasserstein space and explain how these results lead to qualitative and quantitative results for associated interacting agent models. This is joint work with Samuel Daudin (Universite Paris-Cite) and Joe Jackson (University of Chicago).